Fast implementation of two-dimensional APES and CAPON spectral estimators

The matched-filterbank spectral estimators APES and CAPON have recently received considerable attention in a number of applications. Unfortunately, their computational complexity tends to limit their usage in several cases - a problem that has previously been addressed by different authors. In this paper, we introduce a novel approach to the computation of the APES and CAPON spectra, which leads to a computational method that is considerably faster than all existing techniques. The new implementations of APES and CAPON are called fast APES and fast CAPON, respectively, and are developed for the two-dimensional case, with the one-dimensional case as a special case. Numerical examples are provided to demonstrate the application of APES to synthetic aperture radar (SAR) imaging, and to illustrate the reduction in computational complexity provided by our method.